document.write( "Question 314210: How many times can the word \"DEFENSE\" be arranged using permutation or combination? And which one do you use? \n" ); document.write( "
Algebra.Com's Answer #224629 by Edwin McCravy(20056)\"\" \"About 
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document.write( "If the three E's were colored difference, like this\r\n" );
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document.write( "DEFENSE, the answer would be 7P7 or 7! since there are 7 letters.\r\n" );
document.write( "However, for example take the arrangement:\r\n" );
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document.write( "SNEFEED\r\n" );
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document.write( "If the E's were colored differently and we could tell the difference \r\n" );
document.write( "then we could rearrange the colored E's around and the following 6 \r\n" );
document.write( "would all be different:\r\n" );
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document.write( "SNEFEED\r\n" );
document.write( "SNEFEED\r\n" );
document.write( "SNEFEED\r\n" );
document.write( "SNEFEED\r\n" );
document.write( "SNEFEED\r\n" );
document.write( "SNEFEED\r\n" );
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document.write( "The reason there are 6 is because there are 3P3 = 3! ways the E's can\r\n" );
document.write( "be rearranged as above.  So the answer 7! = 5040 is too large a numbee\r\n" );
document.write( "because every arrangement is counted 3! = 6 times too many.  So we must\r\n" );
document.write( "divide 7! by 3! to get the correct answer.  So the answer is\r\n" );
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document.write( "  \r\n" );
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document.write( "Edwin
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